$A$ radio-isotope has a half-life of $5$ years. The fraction of the atoms of this material that would decay in $15$ years will be

In an old rock,the ratio of uranium to lead nuclei is $1:1$. The half-life of uranium is $4.5 \times 10^9$ years. If the rock initially contained only uranium nuclei,how old is the rock?

Find the time in years required for $10\%$ of a radioactive sample to decay,given that its half-life is $22 \text{ years}$.

If a radioactive material remains $25 \%$ after $16$ days,then its half-life will be ......... days.

$A$ radioactive sample is undergoing $\alpha$ decay. At any time $t_{1}$,its activity is $A$ and at another time $t_{2}$,the activity is $\frac{A}{5}$. What is the average life time for the sample?

$A$ radioactive element has a rate of disintegration of $9000$ disintegrations per minute at a particular instant. After $2$ minutes, it becomes $3000$ disintegrations per minute. The decay constant per minute is: